A.2 · IB Physics
Circular motion
An object moves at constant speed round a circle. Change the radius, speed and mass and read how the centripetal force, period and acceleration respond, then see why a constant speed still means a changing velocity.
Predict first
Start from the default settings (r = 6.0 m, v = 5.0 m s⁻¹, m = 2.0 kg). If you double the speed to 10.0 m s⁻¹, what happens to the centripetal force F?
F = mv²/r, so F is proportional to v². Doubling v multiplies F by 2² = 4, giving 33.3 N when m and r are unchanged.
Check it in the model: Move the Speed, v slider from 5.0 to 10.0 m s⁻¹ and compare the Force F = mv²/r readout.
velocity v (tangent) centripetal force F (to centre)velocity after a 30° turn
Presets
a = v² ÷ r = ω² r
ω = v ÷ r ; T = 2πr ÷ v
Try this
- At the defaults, raise the speed from 5.0 to 10.0 m s⁻¹. By what factor do the force and the period change? Check against F = mv²/r and T = 2πr/v.
- Tick “Show how v changes”. Watch the red Δv arrow as the object moves: which way does it point, and how does Δv/Δt compare with a = v²/r?
- Use the Heavy object preset, then halve the radius from 6.0 to 3.0 m. Does the force double or quadruple, and what happens to ω?
Common error: the centripetal force is not an extra force: it is the name for the resultant of the real forces (tension, friction, gravity) pointing to the centre, and there is no outward “centrifugal force” to add to a free-body diagram.